x=5x2-6/2=8

Solution for x=5x2-6/2=8 equation:

X=5X^2-6/2=8

We move all terms to the left:

X-(5X^2-6/2)=0

We get rid of parentheses

-5X^2+X+6/2=0

We multiply all the terms by the denominator


-5X^2*2+X*2+6=0

Wy multiply elements

-10X^2+2X+6=0

a = -10; b = 2; c = +6;
Δ = b2-4ac
Δ = 22-4·(-10)·6
Δ = 244
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{61}}{2*-10}=\frac{-2-2\sqrt{61}}{-20}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{61}}{2*-10}=\frac{-2+2\sqrt{61}}{-20}
$